Question 5057
{{{ (x^4 - 4x^3 + 3x) / (x^2 - 1)}}}


First factor out the x from the numerator, and factor the denominator:
{{{ (x(x^3 - 4x^2 + 3) )/ ((x - 1)(x+ 1) )  }}}


Now the trick is this:  Is {{{ x^3 - 4x^2 + 3 }}} divisible by either (x-1) or (x+1).  It turns out (and it usually does!) that it is, in this case, divisible by (x-1).  You will have to do synthetic or polynomial division (which I don't know how to do on this website!) as follows:

Divide:
1 |   1   -4   0   3
XXX           1  -3  -3
_____________________ 
XX      1   -3  -3   0


Other tutors could probably write it better, but basically, the remainder is zero, and the quotient is {{{x^2 - 3x - 3}}}


Therefore the x-1 divides out leaving this:

{{{ (x(x-1) (x^2 - 3x - 3) )/ ((x - 1)(x+ 1) )  }}}

{{{ (x (x^2 - 3x - 3) )/ (x+ 1) }}}


By the way, the remaining trinomial does not factor.


R^2 at SCC